**Peter J.-S. Shiue, Anthony G. Shannon, Shen C. Huang, Jorge E. Reyes**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 1, Pages 98–129

DOI: 10.7546/nntdm.2023.29.1.98-129

**Full paper (PDF, 388 Kb)**

## Details

### Authors and affiliations

Peter J.-S. Shiue

*Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154, United States of America
*

Anthony G. Shannon

*Warrane College, University of New South Wales
Kensington, NSW 2033, Australia*

Shen C. Huang

*Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154, United States of America
*

Jorge E. Reyes

*Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154, United States of America
*

### Abstract

A generalized Computation procedure for construction of the Ramanujan-type from a given general cubic equation and a cosine Ramanujan-type identity is developed from detailed analyses of the properties of Ramanujan-type cubic equations. Examples are provided together with cubic Shevelev sums.

### Keywords

- Ramanujan cubic polynomials
- Ramanujan cubic polynomials of the second kind
- Cubic Shevelev sum

### 2020 Mathematics Subject Classification

- 11C08
- 11D25
- 11Y99

### References

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### Manuscript history

- Received: 25 December 2022
- Revised: 28 February 2023
- Accepted: 2 March 2023
- Online First: 6 March 2023

### Copyright information

Ⓒ 2023 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

## Related papers

- Shiue, P. J.-S., Shannon, A. G., Huang, S. C., & Reyes, J. E. (2022). Notes on efficient computation of Ramanujan cubic equations.
*Notes on Number Theory and Discrete Mathematics*, 28(2), 350–375. - Wang, K. (2021). On Ramanujan type identities and Cardano formula.
*Notes on Number Theory and Discrete Mathematics*, 27(3), 155–174.

## Cite this paper

Shiue, P. J.-S., Shannon, A. G., Huang, S. C., & Reyes, J. E. (2023). A generalized computation procedure for Ramanujan-type identities and cubic Shevelev sum. *Notes on Number Theory and Discrete Mathematics*, 29(1), 98-129, DOI: 10.7546/nntdm.2023.29.1.98-129.